Nice job on the re-work. Especially for reducing the height of the speed-bump that is technology that keeps some of my peers from using your materials. Will pass new version along to rest of my department.

Scott:

0. Slide 4, justify quadratic via gravity? or no? leave to teacher?

Done. Don’t want the selection of the new model to seem arbitrary.

1. Prediction slides— seems awkward to rely on paper when it is theoretically possible to grab the S responses. This wouldn’t be normal behavior for activity builder, but I’m sure you can ask about feasibility :)

Yeah, we’re currently working on a data transportation layer that would make this sort of copy forward possible. Stay tuned. #staytuned

Analyze slides— encourage more descriptive predictions?

I added “and why?” to the questions, though it’s up to the teacher to encourage that level of analysis, I think.

Kevin:

Regarding what Howard said, I worry a little that this activity reinforces students’ misconception that a graph of motion is a picture of the path that the object took. You see this misconception in Function Carnival a lot.

I agree that’s a risk. But I’m more inclined to offer students a variety of quadratic models rather than shy from any one model in particular.

Adam Poetzel:

So when will the Desmos Activity Builder allow for users to upload videos for students to watch and respond to??? :)

Yeah, I’m kind of missing the videos here also. #staytuned

Students could be given the same type of basketball pictures without the draggable parabola and be asked to write their own equation that they think best matches the ball path. They can use their own graph to make their predictions.

Yeah, I love it. I figured I’d use an activity like that towards the end of the unit. “Instead of fiddling, now deduce the model.” Last week I shot a bunch more basketball shots, though, so students wouldn’t invest the effort in shots they’ve already answered.

Interesting questions from Kevin about the sequencing of this lesson. I think option (C) is closest to my route. We need this new model for reasons established in this activity. There are different algebraic forms of this new model. We need to put students into situations to understand when one form is more useful than another. The details of that plan are left as an exercise to … oh shoot — me. I have to figure this out now.

If you choose (A), this lesson seems great, but we need something else to motivate kids to study multiplying and factoring expressions first. I know you did a summer post about making a headache for which factoring could be the aspirin–and maybe that would be enough–but honestly what the community came up with there wasn’t nearly as engaging as Will It Hit The Hoop. Until kids see that quadratic expressions can model a huge swath of life, they might not see the point of the tedium involved in factoring. (In the blog post I referenced in my comment above, I talk about showing this huge swath of life as reaching a mathematical vista). Again, this is not a critique of Will It Hit The Hoop. It’s great! I’m asking where people see this excellent lesson fitting into a broader unit plan.

If you choose (B), you’d be telling kids that Will It Hit The Hooop shows why expressions with x^2 are important and then stepping away from all the content of the lesson (parabolas) to go back and do factoring and multiplying. In this case, you may waste much of the learning that this lesson creates. The main math content of Will It Hit The Hoop is intuition for vertex form of a parabola. If you do the lesson and then retreat back to multiplying and factoring expressions, students may have forgotten this intuition by the time you return to parabolas.

Perhaps there’s an option (C): teach parabolas with vertex form and standard form first, and then go back and do multiplying and factoring so you can study factored form of a parabola and find the zeros of the function. Probably throw the quadratic formula in at that point. I’ve never taught it that way, but I’m curious what others do/think.